TNT equivalent

Diagram of explosive yield vs mushroom cloud height, illustrating the difference between 22 kiloton Fat Man and 15 megaton Castle Bravo explosions

TNT equivalent is a convention for expressing the energy released in an explosion. The "ton of TNT" is a unit of energy defined by that convention to be 4.184 gigajoules,^[1] which is the approximate energy released in the detonation of a metric ton (1,000 kilograms or one megagram) of TNT. The convention intends to compare the destructiveness of an event with that of ordinary explosives, although TNT is not the most energetic among them. The energy density of dynamite, for example, is approximately 7.5 MJ/kg, about 60% greater than the 4.7 MJ/kg of TNT.

The "megaton of TNT" is a unit of energy equal to 4.184 petajoules.^[2] The kiloton and megaton of TNT have traditionally been used to describe the energy output, and hence the destructive power, of a nuclear weapon. The TNT equivalent appears in various nuclear weapon control treaties, and has been used to characterize the energy released in such other highly destructive events as an asteroid impact.

Historical derivation of the value

A gram of TNT releases 2673 - 6702 J (joules) upon explosion.^[3] The energy liberated by one gram of TNT was arbitrarily defined as a matter of convention to be 4184 J,^[4] which is exactly one kilocalorie.

An explosive's energy is normally expressed as the thermodynamic work produced by its detonation, which for TNT has been accurately measured as 4686 J/g from a large sample of air blast experiments, and theoretically calculated to be 4853 J/g.^[5]

The measured, pure heat output of a gram of TNT is only 2724 J,^[6] but this is not the important value for explosive blast effect calculations.

Alternative TNT equivalency can be calculated as a function of when in the detonation the value is measured and which property is being compared.^{[7][8][9][10]}

A kiloton of TNT can be visualized as a cube of TNT 8.46 metres (27.8 ft) on a side.

Grams TNT	Symbol	Tons TNT	Symbol	Energy	Corresponding mass loss
gram of TNT	g	microton of TNT	μt	4.184×10^3 J or 4.184 kilojoules	46.55 pg
kilogram of TNT	kg	milliton of TNT	mt	4.184×10^6 J or 4.184 megajoules	46.55 ng
megagram of TNT	Mg	ton of TNT	t	4.184×10^9 J or 4.184 gigajoules	46.55 μg
gigagram of TNT	Gg	kiloton of TNT	kt	4.184×10^12 J or 4.184 terajoules	46.55 mg
teragram of TNT	Tg	megaton of TNT	Mt	4.184×10^15 J or 4.184 petajoules	46.55 g
petagram of TNT	Pg	gigaton of TNT	Gt	4.184×10^18 J or 4.184 exajoules	46.55 kg

Conversion to other units

1 ton TNT equivalent is approximately:

• 1.0×10⁹ calories
• 4.184×10⁹ joules
• 3.96831×10⁶ British thermal units
• 3.08802×10⁹ foot pounds
• 1.162×10³ kilowatt hours

Examples

Megatons of TNT	Description
10^-9	Under controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle.
10^-8	The approximate radiant heat energy released during 3-phase, 600 V, 100 kA arcing fault in a 0.5 m × 0.5 m × 0.5 m (20 in × 20 in × 20 in) compartment within a 1-second period.[11]
10^-6–4.4x10^-5	Conventional bombs yield from less than one ton to FOAB's forty four tonnes. The yield of a Tomahawk cruise missile is equivalent to 500 kg of TNT, or approximately 0.55 tons.[12]
2.5x10^-6	An American television show, MythBusters, used 2.5 tons of ANFO to make "homemade" diamonds.
5x10^-4	A real 0.5-kilotonne-of-TNT (2.1 TJ) charge at Operation Sailor Hat. If the charge were a full sphere, it would be 1 kilotonne of TNT (4.2 TJ). 500 tons of TNT (6 by 12 m (20 by 40 ft)) awaiting detonation at Operation Sailor Hat.
1—2 x 10^-3	Estimated yield of the Oppau explosion that killed more than five hundred at a German fertilizer factory in 1921.
2.3x10^-3	Amount of solar energy falling on 4,000 m^2 (1 acre) of land in a year is 9.5 TJ (2,650 MWh) (an average over the Earth's disk).
3x10^-3	The Halifax Explosion in 1917 was the accidental detonation of 3,000 tons of TNT.
8x10^-3	Minor Scale, a 1985 United States conventional explosion, using 4,744 tons of ANFO explosive to provide a scaled equivalent airblast of an eight kiloton (33.44 TJ) nuclear device,[13] is believed to be the largest planned detonation of conventional explosives in history.
1.5–2 x 10^-2	The Little Boy atomic bomb dropped on Hiroshima on August 6, 1945, exploded with an energy of about 15 kilotons of TNT (63 TJ), and the Fat Man atomic bomb dropped on Nagasaki on August 9, 1945, exploded with an energy of about 20 kilotons of TNT (84 TJ). The modern nuclear weapons in the United States arsenal range in yield from 0.3 kt (1.3 TJ) to 1.2 Mt (5.0 PJ) equivalent, for the B83 strategic bomb.
1	The energy contained in one megaton of TNT (4.2 PJ) is enough to power the average American household for 103,474 years.[14] The 30 Mt (130 PJ) estimated upper limit blast power of the Tunguska event could power the aforementioned home for just over 3,104,226 years. To put that in perspective, the energy of that blast could power the entire United States for 3.27 days.[15]
3	The total energy of all explosives used in World War Two (including the Hiroshima and Nagasaki bombs) is estimated to have been three megatons of TNT.
8.6	The energy released by an "average" tropical cyclone in one minute, primarily from water condensation. Winds constitute a quarter of a percent of that energy.[16]
21.5	The complete conversion of 1 kg of matter into pure energy would yield the theoretical maximum (E = mc^2) of 89.8 petajoules, which is equivalent to 21.5 megatons of TNT. No such method of total conversion as combining 500 grams of matter with 500 grams of antimatter has yet been achieved. In the event of proton–antiproton annihilation, approximately 50% of the released energy will escape in the form of neutrinos, which are almost undetectable.[17] Electron–positron annihilation events emit their energy entirely as gamma rays.
25, 50, 100	During the Cold War, the United States developed hydrogen bombs with maximum theoretical yields of 25 megatons of TNT (100 PJ). The Soviet Union developed a prototype weapon, nicknamed the Tsar Bomba, which was tested at 50 Mt (210 PJ), but had a maximum theoretical yield of 100 Mt (420 PJ).[18] The effective destructive potential of such a weapon varies greatly, depending on such conditions as the altitude at which it is detonated, the characteristics of the target, the terrain, and the physical landscape upon which it is detonated.
26.3	Megathrust earthquakes 2004 Indian Ocean earthquake released record ME surface rupture energy, or potential for damage at 26.3 megatons of TNT (110 PJ).
540	The total energy produced worldwide by all nuclear testing and combat combined, from the 1940s till now is about 540 megatons.
7,000	The total global nuclear arsenal is about 30,000 nuclear warheads with a destructive capacity of 7,000 megatons or 7 gigatons (7,000 million tons) of TNT.
62,500	The total solar energy received by Earth per minute is 440 exajoules.
6,000,000 = 6×10^6	The estimated energy at impact when the largest fragment of Comet Shoemaker–Levy 9 struck Jupiter is equivalent to six million megatons (six trillion tons) of TNT.
9.32×10^6	The energy released in the 2011 Tōhoku earthquake and tsunami was over 200,000 times the surface energy and was calculated by the USGS at 3.9×10^22 joules,[19] slightly less than the 2004 Indian Ocean quake. This is equivalent to 9,320 gigatons of TNT, or approximately 600 million times the energy of the Hiroshima bomb.
9.56×10^6	Megathrust earthquakes record huge MW values, or total energy released. The 2004 Indian Ocean earthquake released 9,560 gigatons TNT equivalent.
1×10^8	The approximate energy released when the Chicxulub impact caused the mass extinction sixty six million years ago was estimated to be equal to 100 teratons (i.e. 100 exagrams or approximately 220.462 quadrillion pounds) of TNT. That is roughly eight billion times stronger than each of the bombs that hit Hiroshima and Nagasaki and the most energetic event on the history of Earth for hundreds of millions of years, far more powerful than any volcanic eruption, earthquake or firestorm. Such an explosion annihilated everything within a thousand miles of the impact in a split second. Such energy is equivalent to that needed to power the whole Earth for several centuries.
7.89×10^15	Total solar output in all directions per day.
2.4×10^28–4.8×10^28	On a much grander scale, a type 1a supernova explosion gives off 1–2x10^44 joules of energy, which is about 2.4 to 4.8 hundred billion yottatons (24 to 48 octillion (2.4–4.8x10^28) megatons) of TNT, equivalent to the explosive force of a quantity of TNT over a trillion (10^12) times the mass of the planet Earth. The Type 1a supernova is essentially the fusion detonation of all the fusable fuel in a star of about 1.4 solar masses within a few seconds, and is a standard candle used for intergalactic distance measurements.
2.4×10^30–4.8×10^30	The largest supernova explosions witnessed, so-called Gamma-ray bursts (GRBs) released more than 10^46 joules of energy.[20]

For more, see Orders of magnitude (energy).

See also

• Nuclear weapon yield
• Nuclear arms race
• Orders of magnitude (energy)
• Relative effectiveness factor
• Ton
• Tonne
• Tonne of oil equivalent, a unit of energy almost exactly 10 tonnes of TNT
• Table of explosive detonation velocities

References

1. "Tons (Explosives) to Gigajoules Conversion Calculator". unitconversion.org.
2. "Joules to Megatons Conversion Calculator". unitconversion.org.
3. Blast effects of external explosions (Section 4.8. Limitations of the TNT equivalent method)
4. "Appendix B8 – Factors for Units Listed Alphabetically". In NIST SI Guide 2008
5. Cooper, Paul W. (1996). Explosives Engineering. New York: Wiley-VCH. p. 406. ISBN 0-471-18636-8.
6. Muller, Richard A. (2001–2002). "Chapter 1. Energy, Power, and Explosions". Physics for Future Presidents, a textbook. ISBN 978-1-4266-2459-9.
7. Sorin Bastea, Laurence E. Fried, Kurt R. Glaesemann, W. Michael Howard, P. Clark Souers, Peter A. Vitello, Cheetah 5.0 User's Manual, Lawrence Livermore National Laboratory, 2007.
8. Maienschein, Jon L. (2002). Estimating equivalency of explosives through a thermochemical approach (PDF) (Technical report). Lawrence Livermore National Laboratory. UCRL-JC-147683.
9. Maienschein, Jon L. (2002). Tnt equivalency of different explosives – estimation for calculating load limits in heaf firing tanks (Technical report). Lawrence Livermore National Laboratory. EMPE-02-22.
10. Cunningham, Bruce J. (2001). C-4/tnt equivalency (Technical report). Lawrence Livermore National Laboratory. EMPE-01-81.
11. "Arc blast Tri-Nitro-Toluene TNT Trotyl equivalent - ARCAD INC.". arcblasts.com.
12. "The Ingenuity Gap: Facing the Economic, Environmental, and Other Challenges", Thomas F. Homer-Dixon, p. 249.
13. TECH REPS INC ALBUQUERQUE NM (1986). "Minor Scale Event, Test Execution Report" (PDF).
14. "Frequently Asked Questions – Electricity". United States Department of Energy. 2009-10-06. Retrieved 2009-10-21. (Calculated from 2007 value of 936 kWh monthly usage)
15. "Country Comparison :: Electricity – consumption". The World Factbook. CIA. Retrieved 2009-10-22. (Calculated from 2007 value of 3,892,000,000,000 kWh annual usage)
16. "NOAA FAQ: How much energy does a hurricane release?". National Oceanic & Atmospheric Administration. August 2001. Retrieved 2009-06-30. cites 6e14 watts continuous.
17. Borowski, Stanley K. (March 1996). Comparison of Fusion/Antiproton Propulsion systems (PDF). 23rd Joint Propulsion Conference. NASA Glenn Research Center. doi:10.2514/6.1987-1814. hdl:2060/19960020441.
18. See Currently deployed U.S. nuclear weapon yields, Complete List of All U.S. Nuclear Weapons, Tsar Bomba, all from Carey Sublette's Nuclear Weapon Archive.
19. "USGS.gov: USGS WPhase Moment Solution". Earthquake.usgs.gov. Archived from the original on 13 March 2011. Retrieved 13 March 2011.
20. Maselli, A.; Melandri, A.; Nava, L.; Mundell, C. G.; Kawai, N.; Campana, S.; Covino, S.; Cummings, J. R.; Cusumano, G.; Evans, P. A.; Ghirlanda, G.; Ghisellini, G.; Guidorzi, C.; Kobayashi, S.; Kuin, P.; LaParola, V.; Mangano, V.; Oates, S.; Sakamoto, T.; Serino, M.; Virgili, F.; Zhang, B.- B.; Barthelmy, S.; Beardmore, A.; Bernardini, M. G.; Bersier, D.; Burrows, D.; Calderone, G.; Capalbi, M.; Chiang, J. (2013). "GRB 130427A: A Nearby Ordinary Monster". Science 343 (6166): 48–51. doi:10.1126/science.1242279. PMID 24263134.

• Thompson, A.; Taylor, B.N. (July 2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811. National Institute of Standards and Technology. Version 3.2.
• Nuclear Weapons FAQ Part 1.3
• Rhodes, Richard (2012). The Making of the Atomic Bomb (25th Anniversary ed.). Simon & Schuster. ISBN 978-1-4516-7761-4.